Stabilization of time-delay neural networks via delayed pinning impulses

Abstract

This paper studies the pinning stabilization problem of time-delay neural networks. A new pinning delayed-impulsive controller is proposed to stabilize the neural networks with delays. First, we consider the general nonlinear time-delay systems with delayed impulses, and establish several global exponential stability criteria by employing the method of Lyapunov functionals. Our results are then applied to obtain sufficient conditions under which the proposed pinning controller can exponentially stabilize the time-delay neural networks. It is shown that the global exponential stabilization of delayed neural networks can be effectively realized by controlling a small portion of neurons in the networks via delayed impulses, and, for fixed impulsive control gain, increasing the impulse delay or decreasing the number of neurons to be pinned at the impulsive moments will lead to high frequency of impulses added the corresponding neurons. Numerical examples are provided to illustrate the theoretical results, which demonstrate that our results are less conservative than the results reported in the existing literatures when the proposed pinning controller reduces to the delayed impulsive controller.